Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 93 · 40 sums

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

1. 1.What is √900? =
2. 2.What is √3025? =
3. 3.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
6. 6.A square garden has an area of 25 square m. How long is each side (in m)?
7. 7.What is √2809? =
8. 8.What is √9801? =
9. 9.What is √6400? =
10. 10.What is the smallest whole number by which 24 must be divided to get a perfect square?
11. 11.A square garden has an area of 729 square m. How long is each side (in m)?
12. 12.What is √1024? =
13. 13.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
14. 14.How many whole numbers lie between 37² and 38²?
15. 15.How many whole numbers lie between 42² and 43²?
16. 16.A square garden has an area of 1521 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 1156 (b) 1218 (c) 1161
18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
19. 19.A square garden has an area of 841 square m. How long is each side (in m)?
20. 20.Which of these is a perfect square? (a) 938 (b) 900 (c) 903
21. 21.How many whole numbers lie between 39² and 40²?
22. 22.How many whole numbers lie between 10² and 11²?
23. 23.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
24. 24.What is 92²? =
25. 25.What is 72²? =
26. 26.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
27. 27.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
28. 28.What is 35²? =
29. 29.What is √324? =
30. 30.Which of these is a perfect square? (a) 160 (b) 144 (c) 150
31. 31.What is 16²? =
32. 32.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 63 must be divided to get a perfect square?
35. 35.What is the smallest whole number by which 52 must be divided to get a perfect square?
36. 36.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √289? =
38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √225? =
40. 40.Which of these is a perfect square? (a) 729 (b) 743 (c) 741

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